# Graph Golf

The Order/degree Problem Competition

## Rules 2021

Update 2021-04-20

### Categories

The 2021 competition consists of two categories:

General Graph Category
Find a graph with minimum diameter over all undirected graphs with the number of vertices = n and degree ≤ d. If two or more graphs take the minimum diameter, a graph with minimum average shortest path length (ASPL) over all the graphs with the minimum diameter should be found. For the 2021 competition, the order/degree pairs (n, d) = (40, 5), (432, 12), (512, 18), (1024, 5), (3602, 24), (65536, 64), (158976, 10), (100000, 128) are featured. Note that the graphs can be non-regular.
Host-Switch Graph Category
Find a host-switch graph with minimum host-to-host diameter (h-diameter) over all undirected host-switch graphs with the number of host vertices = n and radix ≤ r. If two or more host-switch graphs take the minimum h-diameter, a host-switch graph with minimum host-to-host average shortest path length (h-ASPL) over all the host-switch graphs with the minimum h-diameter should be found. For the 2021 competition, the order/radix pairs (n, r) = (32, 4), (80, 6), (128, 24), (432, 12), (1281, 21), (3800, 30), (1024, 5), (1024, 10), (4608, 36), (8208, 48), (10000, 10), (10000, 100), (65536, 64) are featured. Note that the host-switch graphs can be non-regular. You can use many switch vertices as you want on the host-switch graph.

### Awards

Each category has two awards:

Widest Improvement Award
The widest improvement award goes to the authors who find the largest number of best solutions. The best solution means a graph with the smallest (h-)diameter, and with the smallest (h-)average shortest path length (ASPL) among those with the same (h-)diameter, for each order/degree(radix) pair. Formally speaking, we calculate score = 1000000k + l, where k is the (h-)diameter and l is the (h-)ASPL, and pick the graph with the lowest score as the best solution.
Deepest Improvement Award
The deepest improvement award goes to the authors who achieve the smallest (h-)ASPL gap over all the order/degree(radix) pairs. The (h-)ASPL gap is calculated as gap = lL, where l is the (h-)ASPL of the graph and L is the lower bound of l calculated as in for general graphs and as in for host-switch graphs.

Only those graphs that complies with the featured order/degree(radix) pair will be nominated for the awards. However, we also accept non-featured graphs and make them exhibited on the ranking page. We encourage you to submit your results no matter if featured or not.

### Schedule and tie-breaking rule

The competition goes through two phases: the closed submission period (before 2021-07-26) and the open submission period (after 2021-07-26). At the beginning, solutions accepted by 2021-07-25 23:59 UTC are reviewed and publicated on 2019-07-26. Afterwards, solutions accepted within a week are reviewed and publicated every Monday. Note that a week begins at Monday 00:00 UTC and ends at Sunday 23:59 UTC. At the end, solutions will be accepted until 2021-10-11 23:59 UTC. The last day will be treated as the same week as 2021-10-04.

The first-to-file rule applies to those graphs with the same (h-)diameter and (h-)ASPL. For each order/degree(radix) pair, if two or more graphs have the same diameter and the same (h-)ASPL, only those graphs publicated at the earliest time will be nominated for the awards. If there are two or more such graphs publicated at the same time, all of them will be nominated.

### Publication

When publicated, the submitted graph file will be made available for downloads. The submitted graphs will also be publicated later at Grpah Bank, which is an open database of interesting graphs developed by the Graph Golf team.

### Important dates

• 2021-04-27: Closed submission period starts
• 2021-07-26: Open submission period starts
• 2021-10-11: Submission period ends (deadline 2021-10-11 23:59:59 UTC)